Pseudorandom Bit Generator Based on Varying Time-Delayed Logistic Map

2014 ◽  
Vol 513-517 ◽  
pp. 1727-1730 ◽  
Author(s):  
Ling Feng Liu ◽  
Suo Xia Miao ◽  
Han Ping Hu ◽  
Ya Shuang Deng
Keyword(s):  
Delay Time ◽  
Statistical Tests ◽  
Logistic Map ◽  
Binary Sequences

In this paper, we propose a kind of pseudorandom bit generator based on varying time delayed logistic map. The variation of delay time is chaotic. The experiments show that the generated binary sequences have good cryptographic properties, and can pass all the well known statistical tests.

IRREGULARLY DECIMATED CHAOTIC MAP(S) FOR BINARY DIGITS GENERATIONS

2009 ◽  
Vol 19 (04) ◽  
pp. 1169-1183 ◽  
Author(s):  
ALI KANSO ◽  
NEJIB SMAOUI
Keyword(s):  
Linear Complexity ◽  
Statistical Tests ◽  
Chaotic Map ◽  
Dynamical Behavior ◽  
Logistic Map ◽  
Binary Sequences ◽  
Threshold Function ◽  
A New Technique ◽  
High Level ◽  
Parameter Values

This paper proposes a new technique for generating random-looking binary digits based on an irregularly decimated chaotic map. We present a class of irregularly decimated chaos-based keystream generators, related to the shrinking generator, for the generation of binary sequences. Each generator consists of two subsystems: a control subsystem and a generating subsystem, where each subsystem is based on a single chaotic map. This chaotic map is presented as a 1-D piecewise chaotic map related to the chaotic logistic map. We conduct an analysis of the dynamical behavior of the proposed map to integrate it as a component in the proposed generators subsystems. The output bits of these keystream generators are produced by applying a threshold function to convert the floating-point iterates of the irregularly decimated map into a binary form. The generated keystream bits are demonstrated to exhibit high level of security, long period length, high linear complexity measure and random-like properties at given certain parameter values. Standard statistical tests on the proposed generators, as well as other keystream generators, are performed and compared.

scholarly journals Modification of the Logistic Map Using Fuzzy Numbers with Application to Pseudorandom Number Generation and Image Encryption

Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 474 ◽  
Author(s):  
Lazaros Moysis ◽  
Christos Volos ◽  
Sajad Jafari ◽  
Jesus M. Munoz-Pacheco ◽  
Jacques Kengne ◽  
...  
Keyword(s):  
Lyapunov Exponent ◽  
Image Encryption ◽  
Fuzzy Numbers ◽  
Statistical Tests ◽  
Logistic Map ◽  
Simple Rule ◽  
Pseudorandom Number ◽  
Bifurcation Diagrams ◽  
Triangular Numbers ◽  
Pseudorandom Number Generation

A modification of the classic logistic map is proposed, using fuzzy triangular numbers. The resulting map is analysed through its Lyapunov exponent (LE) and bifurcation diagrams. It shows higher complexity compared to the classic logistic map and showcases phenomena, like antimonotonicity and crisis. The map is then applied to the problem of pseudo random bit generation, using a simple rule to generate the bit sequence. The resulting random bit generator (RBG) successfully passes the National Institute of Standards and Technology (NIST) statistical tests, and it is then successfully applied to the problem of image encryption.

scholarly journals A New Two-Dimensional Mutual Coupled Logistic Map and Its Application for Pseudorandom Number Generator

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Xuan Huang ◽  
Lingfeng Liu ◽  
Xiangjun Li ◽  
Minrong Yu ◽  
Zijie Wu
Keyword(s):  
Statistical Tests ◽  
Chaotic Map ◽  
Logistic Map ◽  
Security Analysis ◽  
Three Dimensional ◽  
Pseudorandom Number ◽  
Pseudorandom Number Generator ◽  
Number Generator ◽  
Two Dimensional ◽  
Practical Applications

Given that the sequences generated by logistic map are unsecure with a number of weaknesses, including its relatively small key space, uneven distribution, and vulnerability to attack by phase space reconstruction, this paper proposes a new two-dimensional mutual coupled logistic map, which can overcome these weaknesses. Our two-dimensional chaotic map model is simpler than the recently proposed three-dimensional coupled logistic map, whereas the sequence generated by our system is more complex. Furthermore, a new kind of pseudorandom number generator (PRNG) based on the mutual coupled logistic maps is proposed for application. Both statistical tests and security analysis show that our proposed PRNG has good randomness and that it can resist all kinds of attacks. The algorithm speed analysis indicates that PRNG is valuable to practical applications.

scholarly journals The Design and FPGA-Based Implementation of a Stream Cipher Based on a Secure Chaotic Generator

2021 ◽  
Vol 11 (2) ◽  
pp. 625
Author(s):  
Fethi Dridi ◽  
Safwan El Assad ◽  
Wajih El Hadj Youssef ◽  
Mohsen Machhout ◽  
René Lozi
Keyword(s):  
Stream Cipher ◽  
Chaotic Maps ◽  
Statistical Tests ◽  
Chaotic Map ◽  
Logistic Map ◽  
Tent Map ◽  
First Order ◽  
Recursive Filters ◽  
Weakly Coupled ◽  
Chebyshev Map

In this study, with an FPGA-board using VHDL, we designed a secure chaos-based stream cipher (SCbSC), and we evaluated its hardware implementation performance in terms of computational complexity and its security. The fundamental element of the system is the proposed secure pseudo-chaotic number generator (SPCNG). The architecture of the proposed SPCNG includes three first-order recursive filters, each containing a discrete chaotic map and a mixing technique using an internal pseudo-random number (PRN). The three discrete chaotic maps, namely, the 3D Chebyshev map (3D Ch), the 1D logistic map (L), and the 1D skew-tent map (S), are weakly coupled by a predefined coupling matrix M. The mixing technique combined with the weak coupling technique of the three chaotic maps allows preserving the system against side-channel attacks (SCAs). The proposed system was implemented on a Xilinx XC7Z020 PYNQ-Z2 FPGA platform. Logic resources, throughput, and cryptanalytic and statistical tests showed a good tradeoff between efficiency and security. Thus, the proposed SCbSC can be used as a secure stream cipher.

scholarly journals On Statistical Testing of Block Ciphers

2018 ◽  
pp. 35-56 ◽  
Author(s):  
P. G. Klyucharev
Keyword(s):  
Statistical Tests ◽  
Random Sequence ◽  
Block Ciphers ◽  
Statistical Test ◽  
Binary Sequences ◽  
Statistical Testing ◽  
Pseudorandom Sequences ◽  
Test Technique ◽  
Cryptographic Algorithms ◽  
Definition Of

Block ciphers form one of the main classes of cryptographic algorithms. One of the challenges in development of block ciphers, like any other cryptographic algorithms, is the analysis of their cryptographic security. In the course of such analysis, statistical testing of block ciphers is often used. The paper reviews literature on statistical testing of block ciphers.The first section of the paper briefly and informally discusses approaches to the definition of the concept of a random sequence, including the Kolmogorov, von Mises, and Martin-Löf approaches and the unpredictability-related approach. However, all these approaches to the definition of randomness are not directly applicable in practice.The second section describes statistical tests of binary sequences. It provides brief descriptions of the tests included in the DieHard, NIST STS, RaBiGeTe statistical test suites.The third section provides the appropriate information to present further the operation modes of block ciphers.The fourth section deals with techniques for statistical testing of block ciphers. Usually such techniques lie in the fact that based on the block cipher under test, various generators of the pseudorandom sequences are built, with their output sequences being tested using any suite of statistical tests. The approaches to the construction of such generators are given.The paper describes the most known statistical test technique for block ciphers among the submitted for the AES competition. It is a technique the NIST uses for statistical testing of ciphers. In addition, there are other techniques mentioned in the literature.In conclusion the paper states that there is a need to develop new techniques for statistical testing of block ciphers.The paper support was provided from the Russian Foundation for Basic Research in the framework of the research project No. 16-07-00542 supported

scholarly journals An image encryption scheme employing key related skipping

2018 ◽  
Vol 69 (2) ◽  
pp. 93-105 ◽  
Author(s):  
Jakub Oravec ◽  
Ján Turán ◽  
L’uboš Ovseník ◽  
Tomáš Huszaník
Keyword(s):  
Phase Space ◽  
Image Encryption ◽  
Statistical Tests ◽  
Logistic Map ◽  
Encryption Algorithm ◽  
Encryption Scheme ◽  
Image Pixels ◽  
Encrypted Images ◽  
Image Encryption Algorithm ◽  
Chaotic Logistic Map

Abstract This paper describes an image encryption algorithm which utilizes chaotic logistic map. Values generated by this map are used in two steps of algorithm which shuffles image pixels and then changes their intensities. Design of the encryption scheme considers possibility of various attacks, such as statistical, differential or phase space reconstruction attacks. Robustness against last mentioned type of attacks is introduced by selective skipping of values generated by the map. This skipping depends on key entered by user. The paper also verifies properties of proposed algorithm by common measures and by set of statistical tests that examine randomness of computed encrypted images. Results are compared with other approaches and they are also briefly discussed.

scholarly journals Pseudo Random Binary Sequence Based on Cyclic Difference Set

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1202
Author(s):  
Md. Selim Al Mamun ◽  
Fatema Akhter
Keyword(s):  
Linear Complexity ◽  
Statistical Tests ◽  
Binary Sequence ◽  
Difference Set ◽  
Quadratic Residue ◽  
Binary Sequences ◽  
Online Information ◽  
Security Applications ◽  
Cyclic Difference Set ◽  
Quadratic Nonresidue

With the increasing reliance on technology, it has become crucial to secure every aspect of online information where pseudo random binary sequences (PRBS) can play an important role in today’s world of Internet. PRBS work in the fundamental mathematics behind the security of different protocols and cryptographic applications. This paper proposes a new PRBS namely MK (Mamun, Kumu) sequence for security applications. Proposed sequence is generated by primitive polynomial, cyclic difference set in elements of the field and binarized by quadratic residue (QR) and quadratic nonresidue (QNR). Introduction of cyclic difference set makes a special contribution to randomness of proposed sequence while QR/QNR-based binarization ensures uniformity of zeros and ones in sequence. Besides, proposed sequence has maximum cycle length and high linear complexity which are required properties for sequences to be used in security applications. Several experiments are conducted to verify randomness and results are presented in support of robustness of the proposed MK sequence. The randomness of proposed sequence is evaluated by popular statistical test suite, i.e., NIST STS 800-22 package. The test results confirmed that the proposed sequence is not affected by approximations of any kind and successfully passed all statistical tests defined in NIST STS 800-22 suite. Finally, the efficiency of proposed MK sequence is verified by comparing with some popular sequences in terms of uniformity in bit pattern distribution and linear complexity for sequences of different length. The experimental results validate that the proposed sequence has superior cryptographic properties than existing ones.

scholarly journals COMPUTATION COMPLEXITY DECREASE IN MACHINE EXPERIMENTS AT VERIFICATION OF CRYPTOGRAPHIC ALGORITHMS

2017 ◽  
Vol 2017 (1) ◽  
pp. 144-152
Author(s):  
Оксана Голембиовская ◽  
Oksana Golembiovskaya ◽  
Александр Козачок ◽  
Aleksandr Kozachok ◽  
Михаил Конышев ◽  
...  
Keyword(s):  
Computational Experiment ◽  
Statistical Tests ◽  
Binary Sequences ◽  
Range Limits ◽  
Directed Search ◽  
Computation Complexity ◽  
Random Sequences ◽  
Cryptographic Algorithms ◽  
Additional Procedure ◽  
Analytical Expressions

The problem of obtaining a set of samples for the assessment of cryptographic algorithms quality on the basis of statistical tests use is considered. New properties of Markov binary chains taking into account dependences of probabilities of binary vectors with different length are described. The analytical expressions allowing the computation of dependences of range limits in values of probabilities of multidimen-sional binary random values upon probabilities of bi-nary random values with smaller dimension are of-fered. The reasons for the necessity of an additional procedure of rejection at the simulation of the realiza-tion of Markov binary processes are defined. A method for the directed search of probability values of sets in the distribution of Markov binary sequences allowing the generation of ergodic binary random sequences that allows refusing completely the procedure of rejection is considered. An algorithm realizing a mentioned method possessing a lowered computational complexity in comparison with the wellknown algorithms for the organization of a computational experiment on the investigation of statistical properties of binary random sequences is presented.

scholarly journals BINARY TIME SERIES GENERATED BY CHAOTIC LOGISTIC MAPS

2003 ◽  
Vol 03 (04) ◽  
pp. 529-544 ◽  
Author(s):  
A. J. LAWRANCE ◽  
RODNEY C. WOLFF
Keyword(s):  
Time Series ◽  
Probability Distributions ◽  
Logistic Map ◽  
Joint Probability ◽  
Binary Sequences ◽  
Binary Time Series ◽  
Non Linear ◽  
Pairwise Dependence ◽  
Joint Probability Distributions ◽  
Special Case

This paper examines stochastic pairwise dependence structures in binary time series obtained from discretised versions of standard chaotic logistic maps. It is motivated by applications in communications modelling which make use of so-called chaotic binary sequences. The strength of non-linear stochastic dependence of the binary sequences is explored. In contrast to the original chaotic sequence, the binary version is non-chaotic with non-Markovian non-linear dependence, except in a special case. Marginal and joint probability distributions, and autocorrelation functions are elicited. Multivariate binary and more discretised time series from a single realisation of the logistic map are developed from the binary paradigm. Proposals for extension of the methodology to other cases of the general logistic map are developed. Finally, a brief illustration of the place of chaos-based binary processes in chaos communications is given.

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